So now we have to face up to the distinction between observing how the Universe behaves, and figuring out if there's a unique physical explanation for it. At first sight, it seems like we've destroyed ordinary physics, because surely having an energy density associated with empty space, makes no sense. Maybe, it's not so surprising though. And the physics that one reaches for at the first instance, is the quantum mechanical uncertainty principle. What this says is that perfect knowledge of the position and speed of a subatomic particle is impossible. So effectively, nothing can be completely at rest. Otherwise you'd know exactly where it is, and that it wasn't moving. This is important, if we think about some of the constituents of what seems to be empty space. One of which is electromagnetic radiation. Now you're seeing me because of electromagnetic radiation. What is it? Well, what we say is that the space between us, is filled with electromagnetic field. Now, nobody actually knows what the electromagnetic field is, but it's a thing whose existence we see in the universe. And you're familiar with it probably through the phenomena of lines of force. Probably everybody at school sprinkled iron filings around a magnet and watched the patterns they generated. So, empty space has electromagnetic lines of force in them. And radiation corresponds to waggling those elastic strings as it were. Now, the Uncertainty Principle, though, says we can't have zero oscillation energy in those springs, because that would be like a state of perfect rest. So, in fact, here must be some zero-point energy, as it's called. And just as a consequence of that, it's obvious that it'd be, it would be extremely surprising if the vacuum contained no energy at all. Because it would be inconsistent with what we know about quantum mechanics. So let me now try and convince you that if empty space can have density, it can also have repulsive gravitational properties. This is the same argument as with expansion of the universe. If something moves, kinetic energy tends to reduce as gravity opposes the motion. So a small sphere of matter in expansion, as it grows larger, will move less rapidly, because its gravitational energy has changed, and it drains away the, the kinetic energy. But, if I have a sphere, a vacuum, that expands, then, because the vacuum has a certain amount of mass per unit volume, as the volume is bigger, the mass inside is correspondingly larger. And that means that the gravitational effects, rather than becoming smaller as the sphere, gets larger, become even bigger. And the only way to conserve energy is for the kinetic energy to rise in addition. So here, M is fixed for ordinary matter. Here, the mass rises in proportion to the volume for the vacuum. And it's this that gives us the tendency to, for the expansion of the universe to accelerate. So now a picture will be, that's the size of the universe versus time, emerges with a big bang, tends to decelerate, but then, goes through an inflection. Because at late times, the vacuum energy dominates. And we seem to live more or less where this inflection is happening, right at the present. So what I have given you so far, is more or less the standard consensus approach to cosmology. But some skepticism is clearly in order. Because the conclusions that we reach about the existence of dark matter, about the existence of dark energy, clearly depend on the physics that we assume. So it's possible that the, the laws of physics that have been assumed, are simply incorrect. After all, the law of gravitation for example, is established by observations on earth or within the solar system. Isn't it a huge extrapolation to think it might apply to the whole universe without modification? Well, other possibilities have been suggested. For example, in terms of getting rid of dark matter, you could consider MOND. Stands for Modified Newtonian Dynamics. What is Newtonian Dynamics? It says F equals M times A. So the force from gravity, dictates the acceleration of particles, how rapidly they change their speed. But if you think about galaxy rotation curves, that's at large distances from the center of the galaxy, the accelerations are much lower than we've ever measured in the laboratory. So, MOND suggests that maybe this fails for the low accelerations. That theory could actually account perfectly well for the rotation curves of galaxies. Similarly, we can get rid of dark energy, which we reached as a conclusion by adopting the Friedmann Equation, which comes from Einstein's gravity. So, if we simply said that Einstein's gravity was not the correct theory dark energy might not exist as a physical substance. It could be simply an optical illusion. So how do we decide, which we believe? Do we take conventional physics with dark matter and dark energy, or do we modify the physics? Are these approaches completely equivalent? Not necessarily. One thing you can do is you can look for consistency. That is, you can ask whether a changed theory could actually explain other things that the old theory couldn't explain. So for example, in the case of dark energy we have not only the size of the universe as the function of time to explain. But we also have the growth under gravity, the collapse under gravity of the patterns in the three-dimensional distribution of galaxies. So this sort of thing can be measured, and you could ask whether it occurs at the correct rate for standard Einstein gravity. Which it does at the level of precision we can probe so far. So, this tends to favour a conventional approach to gravity as opposed to modifying Einstein's theory, for example. But there's an alternative way of, of thinking about this which is less to do with direct tests, because obviously there can only be a finite number of tests of a theory. It has to do with prejudice, and in science there's a well defined probabilistic framework for trying to assess credibility of theories, which goes under the heading of Bayes' theorem in statistics. Now what this does is it turns a degree of belief, which should be a personal quantity, into a probability, which can be quantified, and subject to the usual rules of combining probabilities. What Bayes' theorem says, is that the thing that we would like to know, which is the probability of a theory being true, given the existence of some data, is proportional to the probability of getting that set of data, given that the theory is true, times a prior probability, a degree of plausibility, if you'd like. From this point of view, one can see why it is that the scientific community is reluctant to adopt radical new modes of explanation like MOND. It might do a perfectly good job of accounting for the observations. If we assume MOND we can certainly account for galaxy rotation curves. But MOND is a theory that was created purely to explain one particular astronomical observation. Whereas standard gravity, of course, grows out of a whole range of observations here on Earth or in the solar system. So, therefore, the prior probability of MOND, its general plausibility, seems much lower to most physicists. And this is why the burden of proof for new theories is very high. And it seems to be correct, because we have to account for the fact that one brings prejudices, or experience with efficiency of physics in other contexts. And that has to be included into such a framework before a paradigm shift will actually happen, and a new theory be considered to be more probable in the context of the data. In concluding this quick run down of the modern picture of cosmology, with dark matter and dark energy, you might wonder if any of these ideas have any lasting value. After all, societies throughout history have had their ideas about the nature of the universe. Is this just another passing creation myth that will be laughed at in a thousand years? In the same way as we pour scorn on those who thought that the world was a plate supported on the back of a giant turtle. I would argue not. It's not that we're any cleverer than the Ancients, but we're fortunate to benefit from technology; telescopes large enough to show us a significant fraction of the entire visible universe. The maps that we've made won't change. They have high enough fidelity now that we can see the universe the way it really is. And people have been waiting for this technology to arrive throughout history. We're lucky enough to be the ones here on the spot to use it.
